On a lemma of L. Lorch and D. J. Newman

Abstract

In [6], Lorch and Newman proved the following lemma:Ifg(u)is continuous and of bounded variation, 0 ≦ u ≦ 1, then(1). This was extended more recently by Leviatan and Lorch ([5], Lemma 3) to functions which are of bounded variation on the positive real axis, where non the upper limit of integration on the inner integral is infinite.